Pith Number

pith:WJIBMQ2R

pith:1999:WJIBMQ2R7BZ3ZNF4YCRVFWVCK5

not attested not anchored not stored refs pending

The global quantum duality principle

Fabio Gavarini

arxiv:math/9912186 v2 · 1999-12-22 · math.QA · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WJIBMQ2R7BZ3ZNF4YCRVFWVCK5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:45:01.999096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b250164351f873bcb4bcc0a352daa257683ef20c8e02e05adffa63f300e393b4

Aliases

arxiv: math/9912186 · arxiv_version: math/9912186v2 · doi: 10.48550/arxiv.math/9912186 · pith_short_12: WJIBMQ2R7BZ3 · pith_short_16: WJIBMQ2R7BZ3ZNF4 · pith_short_8: WJIBMQ2R

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WJIBMQ2R7BZ3ZNF4YCRVFWVCK5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b250164351f873bcb4bcc0a352daa257683ef20c8e02e05adffa63f300e393b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6bbb39322089eb5fa3369c0972a7e3f81447cae55554469649798c62ffc7978",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "1999-12-22T15:33:10Z",
    "title_canon_sha256": "bb2221f2c7b975715d69ba903710915bec501f61eff6ae6f19c13e8801e85ad1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912186",
    "kind": "arxiv",
    "version": 2
  }
}